Hi, hadi_xman!
I've had the same problem yesterday - after moving the /var/folders/zz folder to Trash and restarting i've got the hanging startup screen with Apple logo and the progression bar stuck at about 40% or 50%. By the way, it was impossible to boot in safe mode, but the recovery tool (Cmd-R after turn-on) was still working. Re-installing the OS through it gave nothing.
You'll need at least 16 GB USB-Flash drive (or HDD/SSD), an internet connection and your user password to perform the recovery.
Enter the recovery tool after start-up and install the OS using internet connection on the USB-Drive. It took about 30 min for me. Note, that in my case Mac stuck at the end of the installation process - I just turned it off (holding the power button for 10 sec) and after turning it on again the "new" system boots normally from the USB. The boot from the Macintosh HD was still impossible for that moment and even the disk/permissions repair procedure from "new" OS gave nothing.
Now, the idea is to move the deleted /var/folders/zz from trash to it's native location.
At first you'll need to make the hidden folders visible. Enter the terminal and paste the
defaults write com.apple.finder AppleShowAllFiles -boolean true ; killall Finder
string to it, then press Enter. Now you have everything in sight.
Go to Macintosh HD/Users/*Username*/Trash folder (click "Open in new tab" in Finder to open it) - hopefully you'll see the previously deleted "zz" folder. If it is read only and can't be opened, then right-click on it, select the "Get Info" button and make the "Read & Write" privileges for "System", "Wheel" and "Everyone" in "Sharing & Permissions" there. To do this, unlock the window by clicking on the padlock icon in the right-down corner and enter the user password.
I've got five subfolders in "zz" folder in trash, that were named like:
zyxvpxvq6csfxvn_n00000b000002r
zyxvpxvq6csfxvn_n00000bh00002w
zyxvpxvq6csfxvn_n00000s0000068
zyxvpxvq6csfxvn_n00000sm00006d
zyxvpxvq6csfxvn_n000006w00001q
Make sure to copy them in a safe place (on the USB drive, for example).
After that go to Macintosh HD/Private/Var/Folders/zz hidden folder (NOT the same located on your USB!) and check it. I've got all the mentioned subfolders in it and another one with the different name. Delete all of the subfolders which names are identical to those you've got from trash before and leave all of the other subfolders. Then paste the previously saved (in a safe place) subfolders in the "zz" folder.
Go to "Startup Disk" app and check the Macintosh HD to boot from (NOT the USB) and press restart.
After that you'll get your original OS normally boot.
That worked for me.